# Electric field acting on the source charge

• Mayan Fung
In summary, the conversation discusses using Gauss's law to find the force acting on the northern hemisphere of a uniformly charged sphere by the southern hemisphere. The approach involves breaking down the northern hemisphere into tiny fractions and calculating the forces acting on each fraction, including the force from the southern hemisphere and the internal forces between fractions. It is argued that the force acting on the northern hemisphere is ultimately coming from the southern hemisphere, as the internal forces cancel each other out.
Mayan Fung
I am reading Griffith's textbook on EM. There is a problem asking to find the force acting on the northern hemisphere by the southern hemisphere of a uniformly charged sphere.

The solution idea is to find the expression of the E field by Gauss's law and integrate the force over the northern hemisphere. However, part of the total electric field is contributed by the northern hemisphere itself. In my understanding, we should not include the electric field of the object we are calculating the force on it. I wonder why we can solve this problem with this approach?

Chan Pok Fung said:
In my understanding, we should not include the electric field of the object we are calculating the force on it.
I think you are thinking of point particles.

There is a straight-forward explanation if we break down the process of "calculating the force":

- In order to calculate the force acting on the Northern Hemisphere (NH), we can break the NH down into tiny fractions and calculate the "forces that act on each of those fractions", including:
--> The force that the Southern Hemisphere (SH) act on the fraction
--> The forces between NH fractions

- Then, we can calculate the force that act on the HM by adding all the "forces that act on each of those fractions". In doing so, we will have two sums:
--> Total force that the SH act on all the fractions of NH
===> This is the force that SH act NH as a whole
--> Total force of interaction between NH fractions
===> According to Newton's Third Law of Motion, every force has a counter-force, so the sum of the internal forces of all those fractions would ultimately add up to zero.

In short, we can claim that the force acting on the NH was from the SH (although there are internal interaction in the NH, those interactions canceled each other).

starprince, Mayan Fung, vanhees71 and 1 other person
Vinh Nguyen said:
There is a straight-forward explanation if we break down the process of "calculating the force":

- In order to calculate the force acting on the Northern Hemisphere (NH), we can break the NH down into tiny fractions and calculate the "forces that act on each of those fractions", including:
--> The force that the Southern Hemisphere (SH) act on the fraction
--> The forces between NH fractions

- Then, we can calculate the force that act on the HM by adding all the "forces that act on each of those fractions". In doing so, we will have two sums:
--> Total force that the SH act on all the fractions of NH
===> This is the force that SH act NH as a whole
--> Total force of interaction between NH fractions
===> According to Newton's Third Law of Motion, every force has a counter-force, so the sum of the internal forces of all those fractions would ultimately add up to zero.

In short, we can claim that the force acting on the NH was from the SH (although there are internal interaction in the NH, those interactions canceled each other).

That's very clear. Thanks!

starprince, Dale and Vinh Nguyen

## 1. What is an electric field?

An electric field is a physical quantity that describes the influence of electric forces on a charged particle. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How does an electric field act on a source charge?

An electric field exerts a force on a source charge, either attracting or repelling it depending on the charge of the source and the charge of the particle. The force is proportional to the magnitude of the charge and the strength of the electric field.

## 3. What factors affect the strength of an electric field?

The strength of an electric field is affected by the distance from the source charge, the magnitude of the source charge, and the medium through which the electric field is traveling. It is also affected by the presence of other charges in the vicinity.

## 4. How is the direction of an electric field determined?

The direction of an electric field is determined by the direction that a positive test charge would move if placed in the field. It is always directed away from positive charges and towards negative charges.

## 5. What is the equation for calculating the strength of an electric field?

The strength of an electric field is calculated using the equation E = kQ/r^2, where E is the electric field strength, k is the Coulomb's constant, Q is the magnitude of the source charge, and r is the distance from the source charge.

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